Construction of precise confidence sets of disease gene locations after initial identification of linked regions can improve the efficiency of the ensuing fine mapping effort. We took the confidence set inference, a framework proposed and implemented using the Mean test statistic CSI-Mean and improved the efficiency substantially by using a likelihood ratio test statistic CSI-MLS. The CSI framework requires knowledge of some disease-model-related parameters. In the absence of prior knowledge of these parameters, a two-step procedure may be employed: 1 the parameters are estimated using a coarse map of markers; 2 CSI-Mean or CSI-MLS are applied to construct the confidence sets of the disease gene locations using a finer map of markers, assuming the estimates from Step 1 for the required parameters. In this article we show that the advantages of CSI-MLS over CSI-Mean, previously demonstrated when the required parameters are known, are preserved in this two-step procedure, using both the simulated and real data contributed to Problems 2 and 3 of Genetic Analysis Workshop 15. In addition, our result suggests that microsatellite data, when available, should be used in Step 1. Also explored in detail is the effect of the absence of parental genotypes on the performance of CSI-MLS.